login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A004104 Number of self-dual signed graphs with n nodes. Also number of self-complementary 2-multigraphs on n nodes.
(Formerly M1649)
5
1, 1, 2, 6, 20, 86, 662, 8120, 171526, 5909259, 348089533, 33883250874, 5476590066777, 1490141905609371, 666003784522738152, 509204473666338077658, 636051958071749028811326, 1375164117171886868027357906, 4844133410739656724629165903483, 29777568550007746192195431057341474 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

A 2-multigraph is similar to an ordinary graph except there are 0, 1 or 2 edges between any two nodes (self-loops are not allowed).

Of a(1) through a(22) only a(3) = 2 is prime. - Jonathan Vos Post, Feb 19 2011

REFERENCES

F. Harary and R. W. Robinson, Exposition of the enumeration of point-line-signed graphs, pp. 19 - 33 of Proc. Second Caribbean Conference Combinatorics and Computing (Bridgetown, 1977). Ed. R. C. Read and C. C. Cadogan. University of the West Indies, Cave Hill Campus, Barbados, 1977. vii+223 pp.

R. W. Robinson, personal communication.

R. W. Robinson, Numerical implementation of graph counting algorithms, AGRC Grant, Math. Dept., Univ. Newcastle, Australia, 1976.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..50 (terms 1..22 from R. W. Robinson)

Frank Harary, Edgar M. Palmer, Robert W. Robinson, Allen J. Schwenk, Enumeration of graphs with signed points and lines, J. Graph Theory 1 (1977), no. 4, 295-308.

R. W. Robinson, Notes - "A Present for Neil Sloane"

R. W. Robinson, Notes - computer printout

PROG

(PARI)

permcount(v) = {my(m=1, s=0, k=0, t); for(i=1, #v, t=v[i]; k=if(i>1&&t==v[i-1], k+1, 1); m*=t*k; s+=t); s!/m}

edges(v) = {sum(i=2, #v, sum(j=1, i-1, if(v[i]*v[j]%2==0, gcd(v[i], v[j])))) + sum(i=1, #v, if(v[i]%2==0, v[i]\4*2))}

a(n) = {my(s=0); forpart(p=n, s+=permcount(p)*3^edges(p)); s/n!} \\ Andrew Howroyd, Sep 16 2018

CROSSREFS

Cf. A004102, A052111, A052112, A052113.

Sequence in context: A177480 A089179 A177483 * A304932 A293032 A241497

Adjacent sequences:  A004101 A004102 A004103 * A004105 A004106 A004107

KEYWORD

nonn,nice

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Vladeta Jovovic, Jan 19 2000

a(18)-a(20) added by Andrew Howroyd, Sep 16 2018

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 19 14:21 EDT 2018. Contains 316362 sequences. (Running on oeis4.)